Question

limite de raiz de x ao cubo menos raiz de 2 ao cubo sobre x menos 2 quando X tende a 2
​

Answer 1

Resposta:

Lim  (√x³-√2³)/(x-2)

x-->2

(a-b)³=a³-3a²b+3ab²-b³

(a-b)³=a³-b³-3ab(a-b)

a³-b³=(a-b)*[(a-b)²+3ab]

a³-b³=(a-b)*(a²+ab+b³)

Fazendo a=√x  e b=√2

√x³-√2³ =(√x-√2)*(√x²+√2 *√x +√2²)

Lim (√x-√2)*(√x²+√2 *√x +√2²)/(x-2)

x-->2

Lim (√x-√2)*(√x²+√2 *√x +√2²)*(√x+√2)/{ (x-2)(√x+√2) }

x-->2

Lim (x-2)*(√x²+√2 *√x +√2²)/{ (x-2)(√x+√2) }

x-->2

Lim(√x²+√2 *√x +√2²)/(√x+√2)

x-->2

=( 2+2+2)/(√2+√2)

=3/√2  é a resposta